Sharp adaptive nonparametric testing for constant volatility
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917444076961792 |
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| author | Brutsche, Johannes Riepl, Lukas |
| author_facet | Brutsche, Johannes Riepl, Lukas |
| contents | Based on discrete observations, we develop a test to infer if the volatility function $σ(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = σ(t)dW_t$ is constant. The testing procedure is shown to be minimax-optimal and adaptive for infill asymptotics and these results entail that a deviation from the null hypothesis of constancy is best measured in terms of the ratio of $σ(t)$ and its $L^2$-average. The derivation of optimal constants requires the construction of hypotheses with height $h(b)$, where the parameter $b$ solves $F_n(b)=0$ for given functions $F_n$. Proving this equation to be solvable for each $n\in\mathbb{N}$ and establishing quantitative bounds of the solutions is built upon the implicit function theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25668 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp adaptive nonparametric testing for constant volatility Brutsche, Johannes Riepl, Lukas Statistics Theory Based on discrete observations, we develop a test to infer if the volatility function $σ(\cdot)$ within the nonparametric Gaussian white noise model $dY_t = σ(t)dW_t$ is constant. The testing procedure is shown to be minimax-optimal and adaptive for infill asymptotics and these results entail that a deviation from the null hypothesis of constancy is best measured in terms of the ratio of $σ(t)$ and its $L^2$-average. The derivation of optimal constants requires the construction of hypotheses with height $h(b)$, where the parameter $b$ solves $F_n(b)=0$ for given functions $F_n$. Proving this equation to be solvable for each $n\in\mathbb{N}$ and establishing quantitative bounds of the solutions is built upon the implicit function theorem. |
| title | Sharp adaptive nonparametric testing for constant volatility |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2604.25668 |